Simplify the following expression: $\dfrac{72t^5}{132t^3}$ You can assume $t \neq 0$.
$ \dfrac{72t^5}{132t^3} = \dfrac{72}{132} \cdot \dfrac{t^5}{t^3} $ To simplify $\frac{72}{132}$ , find the greatest common factor (GCD) of $72$ and $132$ $72 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $132 = 2 \cdot 2 \cdot 3 \cdot 11$ $ \mbox{GCD}(72, 132) = 2 \cdot 2 \cdot 3 = 12 $ $ \dfrac{72}{132} \cdot \dfrac{t^5}{t^3} = \dfrac{12 \cdot 6}{12 \cdot 11} \cdot \dfrac{t^5}{t^3} $ $\phantom{ \dfrac{72}{132} \cdot \dfrac{5}{3}} = \dfrac{6}{11} \cdot \dfrac{t^5}{t^3} $ $ \dfrac{t^5}{t^3} = \dfrac{t \cdot t \cdot t \cdot t \cdot t}{t \cdot t \cdot t} = t^2 $ $ \dfrac{6}{11} \cdot t^2 = \dfrac{6t^2}{11} $